Substrates Michaelis-Menten model

The above rate equation is in agreement with that reported by Madhav and Ching [3]. Tliis rapid equilibrium treatment is a simple approach that allows the transformations of all complexes in terms of [E, [5], Kls and Kjp, which only deal with equilibrium expressions for the binding of the substrate to the enzyme. In the absence of inhibition, the enzyme kinetics are reduced to the simplest Michaelis-Menten model, as shown in Figure 5.21. The rate equation for the Michaelis-Menten model is given in ordinary textbooks and is as follows 11... 

The functioning of enzymes produces phenomena driving the processes which impart life to an organic system. The principal source of information about an enzyme-catalyzed reaction has been from analyses of the changes produced in concentrations of substrates and products. These observations have led to the construction of models invoking intermediate complexes of ingredients with the enzyme. One example is the Michaelis-Menten model, postulating an... 

From the Michaelis-Menten model, there is a relationship between 1/Fo and the initial substrate concentration, expressed as the reciprocal, 1/[Bq]. To develop this relationship we shall repeat Example 9.1 using varying concentrations of B cells. Be sure to subtract the number of Bq cells in each study from the total number of water, D, cells in the setup. 

In kinetic studies of enzymatic reactions, rate data are usually tested to determine if the reaction follows the Michaelis-Menten model of enzyme-substrate interaction. Weetall and Havewala [Biotechnol. and Bioeng. Symposium 3 (241), 1972] have studied the production of dextrose from cornstarch using conventional... 

The three models used are described by Eq. (6-8) below. The Eqn. (6) is the first-order model based on Michaelis-Menten model, Eqn. (7) is the second-order model, and the Eqn. (8) is the competitive-substrate model. Rso represents the initial specific reaction rate for the substrate S. 

The model most often invoked to rationalize cooperative behavior is the MWC (Monod-Wyman-Changeaux), or concerted, model. This model is 1.5 times more complicated than the Michaelis-Menten model and took three people to develop instead of two. Most texts describe it in detail. In the absence of substrate, the enzyme has a low affinity for substrate. The MWC folks say that the enzyme is in a T (for tense or taut) state in the absence of substrate. Coexisting with this low-affinity T state is another conformation of the enzyme, the R (for relaxed) state, that has a higher affinity for substrate. The T and R states coexist in the absence of substrate, but there s much more of the T state than the R. This has always seemed backward, since one would expect the enzyme to be more tense in the presence of substrates when some work is actually required. In keeping with the tradition of biochemistry, the MWC folks obviously wanted this to be backward too (Fig. 8-8). 

STEADY STATE TREATMENT. While the Michaelis-Menten model requires the rapid equilibrium formation of ES complex prior to catalysis, there are many enzymes which do not exhibit such rate behavior. Accordingly, Briggs and Haldane considered the case where the enzyme and substrate obey the steady state assumption, which states that during the course of a reaction there will be a period over which the concentrations of various enzyme species will appear to be time-invariant ie., d[EX]/dr s 0). Such an assumption then provides that... 

The basic kinetic model for enzyme catalysed conversions in water and in w/o-microemulsions is based on the theory of MichaeHs and Menten [83]. Although the Michaelis-Menten-model is often sufficient to describe the kinetics, the bi-bi-models (e. g. random bi-bi, orderedbi-bi or ping-pongbi-bi), which describe the sequences of substrate bindings to the enzyme are the more accurate kinetic models [84]. 

The Michaelis-Menten equation represents a mechanistic model because it is based upon an assumed chemical reaction mechanism of how the system behaves. If the system does indeed behave in the assumed manner, then the mechanistic model is adequate for describing the system. If, however, the system does not behave in the assumed manner, then the mechanistic model is inadequate. The only way to determine the adequacy of a model is to carry out experiments to see if the system does behave as the model predicts it will. (The design of such experiments will be discussed in later chapters.) In the present example, if substrate inhibition occurs, the Michaelis-Menten model would probably be found to be inadequate a different mechanistic model would better describe the behavior of the system. 

Using a similar approach to that used in the derivation of the Michaelis-Menten model, the kinetic equations of the peroxidase-catalyzed removal of an aromatic substrate were derived from the reaction pathways illustrated in Fig. 2 [92]. The rate of change of the aromatic compound concentration can be written as... 

The dynamics were run for several concentrations of substrate and variations in the Pc values. Initial velocities of the reaction were recorded. The Michaelis-Menten model was observed and characteristic Lineweaver-Burk plots were found from the model. Systematic variation of the lipophilicity of substrates and products showed that a lower affinity between a substrate and water leads to more of the S —> P reaction at a common point along the reaction progress curve. This influence is greater than that of the affinity between the substrate and the enzyme. The study created a model in which the more lipophilic substrates are more reactive. The water-substrate affinity appears... 

In this area, recent unrelated efforts of the groups of Bhattacharya and Fife toward the development of new aggregate and polymer-based DAAP catalysts deserve mention. Bhattacharya and Snehalatha [22] report the micellar catalysis in mixtures of cetyl trimethyl ammonium bromide (CTAB) with synthetic anionic, cationic, nonionic, and zwitterionic 4,4 -(dialkylamino)pyridine functional surfactant systems, lb-c and 2a-b. Mixed micelles of these functional surfactants in CTAB effectively catalyze cleavage of various alkanoate and phosphotriester substrates. Interestingly these catalysts also conform to the Michaelis-Menten model often used to characterize the efficiency of natural enzymes. These systems also demonstrate superior catalytic activity as compared to the ones previously developed by Katritzky and co-workers (3 and 4). 

The Michaelis-Menten model accounts for the kinetic properties of some enzymes. In this model, an enzyme (E) combines with a substrate (S) to form an enzyme-substrate (ES) complex, which can proceed to form a product (P) or to dissociate into E and S. 

For carrier-mediated transport of L-lactic acid across human carcinoma cell line, it was found that increasing agitation rate resulted in a larger fractal dimension accompanied by a decrease in the substrate permeability rate. The classical Michaelis-Menten model is known to be only valid for a limited range of glucose concentrations. An alternative model was proposed including convective and non-linear diffusive mechanisms corresponding to the first and second (fractal power function) terms in Eq. (30). 

Rate limiting steps are the molecular processes that effectively limit the rate of the overall reaction. They are the slowest step in the series of steps leading to product formation. The rate limiting step may be examined for an enzyme-catalyzed reaction. For the Michaelis-Menten model, the rate of product formation (or the negative of the rate of substrate loss) is given by ... 

Enzyme kinetics is the quantitative study of enzyme catalysis. According to the Michaelis-Menten model, when the substrate S binds in the acdve site of an enzyme E, an ES transition state complex is formed. During the transition state, the substrate is converted into product. After a time the product dissociates from the enzyme. In the Michaelis-Menten equation,... 

The kinetic properties of allosteric enzymes are not explained by the Michaelis-Menten model. Most allosteric enzymes are multisubunit proteins. The binding of substrate or effector to one subunit affects the binding properties of other protomers. 

This analysis can be applied to enzymatic as well as to simple chemical transformations [9-11], for uni- and multi-substrate [12] reactions according to Eqs. (1) and (2). nNKM denotes the product of Michealis-Menten constants for all substrates. In this analysis one assumes that kinetics follow the Michaelis-Menten model, which is the case for most antibody-catalyzed processes discussed below. The kcat denotes the rate constant for reaction of the antibody-substrate complex, Km its dissociation constant, and kuncat the rate constant for reaction in the medium without catalytic antibody or when the antibody is quantitatively inhibited by addition of its hapten. In several examples given below there is virtually no uncatalyzed reaction. This of course represents the best case. 

This rate equation is called Michaelis-Menten double substrate kinetics . It is a formal multiplication of two Michaelis-Menten models for both substrates A and B. This model can be used to describe rate kinetics of two substrate reactions in the absence of the product(s). The kinetic measurements have to be performed by varying the concentration of one substrate keeping the concentration of the second substrate at a constant value well above the Km value. The model cannot be used if back reactions occur and an equilibrium has to be described by an appropriate Haldane equation. 

Assuming that substrate conversion obeys the simple Michaelis-Menten model, substrate steady state mass balance reduces to ... 

The equations of enzyme kinetics provide a quantitative way of desaibing the dependence of enzyme rate on substrate concentration. The simplest of these equations, the Michaelis-Menten equation, relates the initial velocity (Vj) to the concentration of substrate [S] and the two parametCTS and (Equation 9.1) The of the enzyme is the maximal velocity that can be achieved at an infinite concentration of substrate, and the of the enzyme for a substrate is the concentration of substrate required to reach Vz V iax- The Michaelis-Menten model of enzyme kinetics applies to a simple reaction in which the enzyme and substrate form an enzyme-substrate complex (ES) that can dissociate back to the free enzyme and substrate. The initial velocity of product formation, Vj, is proportionate to the concentration of enzyme-substrate complexes [ES]. As substrate concentration is increased, the concentration of enzyme-substrate complexes increases, and the reaction rate inaeases proportionately. 

Equations for the initial velocity of an enzyme-catalyzed reaction, such as the Michaelis-Menten equation, can provide useful parameters for describing or comparing enzymes. However, many multisubstrate enzymes, such as glucokinase, have kinetic patterns that do not fit the Michaelis-Menten model (or do so under non-physiologic conditions). The Michaelis-Menten model is also inapplicable to enzymes present in a higher concentration than their substrates. Nonetheless, the term K is still used for these enzymes to describe the approximate concentration of substrate at which velocity equals Y2 V ax-... 

In the initial stages of the reaction, so little product is present that no reverse reaction of product to complex need be considered. Thus the initial rate determined in enzymatic reactions depends on the rate of breakdown of the enzyme-substrate complex into product and enzyme. In the Michaelis-Menten model, the initial rate, V, of the formation of product depends only on the rate of the breakdown of the ES complex,... 

Deep knowledge of the enzymatic reaction is necessary for a proper selection of the variables that should be considered in the reaction model. In this case, two variables were selected Orange n concentration, as the dye is the substrate to be oxidized, and H2O2 addition rate, as the primary substrate of the enzyme (Lopez et al. 2007). The performance of some discontinuous experiments at different initial values of both variables resulted in the definition of a kinetic equation, defined using a Michaelis-Menten model with respect to the Orange II concentration and a first-order linear... 

However, the Michaelis-Menten model defines the correlation of biodegradation rates only vs. amount of substrate. It is an individual enzymatic reaction and assumes constant amoxmt of the enzyme, i.e., it does not accoxmt for changes in the amoxmt of microorganisms. In real conditions both concentrations of the substrate and biomass change. 

In kinetic smdies of enzymatic reactions, rate data are usually tested to determine if the reaction follows the Michaelis-Menten model of enzyme-substrate interactions. H. H. WeetaU and N. B. Havewala [Biotechnol. Bioeng. Symp., 3, 241 (1972) studied the production of dextrose from cornstarch using conventional glucoamylase and an immobihzed version thereof. Their goal was to obtain the data necessary to design a commercial facility for dextrose production. Their studies were carried out in a batch reactor at 60°C. Compare the data below with those predicted from a Michaelis-Menten model with a rate expression of the form... 

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